Abstract: In this paper, we express the Mahler measure of a two-variable polynomial P(x,y)=(x²+1)y²+2(x²+x)y+x(x²+1) as a linear sum of some Bloch-Wigner Dilogarithm functions. and prove that the Mahler measure of P(x,y) is rationally proportional to L'(χ_-3,-1):m(P(x,y))=5/2L'(χ_-3,-1).

Key words: Mahler measure, Bloch-Wigner dilogarithm functions, special values of L-functions